https://artofproblemsolving.com/wiki/index.php?title=1955_AHSME_Problems/Problem_23&feed=atom&action=history1955 AHSME Problems/Problem 23 - Revision history2024-03-29T12:26:16ZRevision history for this page on the wikiMediaWiki 1.31.1https://artofproblemsolving.com/wiki/index.php?title=1955_AHSME_Problems/Problem_23&diff=137580&oldid=prevAngrybird029: Created page with "In checking the petty cash a clerk counts <math>q</math> quarters, <math>d</math> dimes, <math>n</math> nickels, and <math>c</math> cents. Later he discovers that <math>x</mat..."2020-11-18T16:57:49Z<p>Created page with "In checking the petty cash a clerk counts <math>q</math> quarters, <math>d</math> dimes, <math>n</math> nickels, and <math>c</math> cents. Later he discovers that <math>x</mat..."</p>
<p><b>New page</b></p><div>In checking the petty cash a clerk counts <math>q</math> quarters, <math>d</math> dimes, <math>n</math> nickels, and <math>c</math> cents. Later he discovers that <math>x</math> of the nickels were counted as quarters and <math>x</math> of the dimes were counted as cents. To correct the total obtained the clerk must:<br />
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<math>\textbf{(A)}\ \text{make no correction}\qquad\textbf{(B)}\ \text{subtract 11 cents}\qquad\textbf{(C)}\ \text{subtract 11}x\text{ cents}\\ \textbf{(D)}\ \text{add 11}x\text{ cents}\qquad\textbf{(E)}\ \text{add }x\text{ cents}</math><br />
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==Solution==<br />
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If the clerk mistook <math>x</math> nickels as quarters, then every mistake inflates the total by <math>20</math> cents. In order to correct this, we have to subtract <math>20</math> cents <math>x</math> times, for a total of <math>20x</math> cents. We can do the same for the <math>x</math> dimes that were turned into pennies (or cents). This exchange would increase the total value of the coins by <math>9x</math>.<br />
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As a total, you get <math>-20x + 9x = -11x</math>. In order to correct the amount, the clerk should <math>\boxed{\text{subtract } 11x \text{ cents}}</math>.<br />
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==See Also==<br />
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{{AHSME 50p box|year=1955|num-b=22|num-a=24}}<br />
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{{MAA Notice}}</div>Angrybird029